Mixing
Generate a prime which divides a prime - 1
0
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I generated a random prime p. Now I want to find a random prime with a fixed size of 256 Bit which divides p - 1.
p has 3072 Bit, so I can't just try it out.
prime-numbers
asked Jan 26 at 19:27
9137824691378246
1
$endgroup$
add a comment |
0
$begingroup$
I generated a random prime p. Now I want to find a random prime with a fixed size of 256 Bit which divides p - 1.
p has 3072 Bit, so I can't just try it out.
prime-numbers
asked Jan 26 at 19:27
9137824691378246
1
$endgroup$
1
$begingroup$
Do you know that such a prime exists in your case? Usually it won't.
$endgroup$
– quid♦
Jan 26 at 19:30
$begingroup$
No, I don't, but I hoped some one knows an algorithm, which could tell me if one exists and, if so, which prime it is.
$endgroup$
– 91378246
Jan 26 at 19:34
1
$begingroup$
@91378246: such algorithm would have solved the factorization problem and broken RSA. Given some large integer (integers of the form $p-1$ are not really special) there is no simple (polynomial) way to get a divisor, but you may employ sieve methods (like the quadratic sieve) to find divisors in some range, then a primality test (AKS is polynomial, for instance) to select prime divisors. Anyway, it will be computationally expensive.
$endgroup$
– Jack D'Aurizio
Jan 27 at 0:47
$begingroup$
Thank you very much, I will look into that.
$endgroup$
– 91378246
Jan 27 at 12:45
add a comment |
0
0
0
$begingroup$
I generated a random prime p. Now I want to find a random prime with a fixed size of 256 Bit which divides p - 1.
p has 3072 Bit, so I can't just try it out.
prime-numbers
asked Jan 26 at 19:27
9137824691378246
1
$endgroup$
I generated a random prime p. Now I want to find a random prime with a fixed size of 256 Bit which divides p - 1.
p has 3072 Bit, so I can't just try it out.
prime-numbers
prime-numbers
asked Jan 26 at 19:27
9137824691378246
1
asked Jan 26 at 19:27
9137824691378246
1
asked Jan 26 at 19:27
9137824691378246
1
asked Jan 26 at 19:27
9137824691378246
1
asked Jan 26 at 19:27
9137824691378246
1
1
1
$begingroup$
Do you know that such a prime exists in your case? Usually it won't.
$endgroup$
– quid♦
Jan 26 at 19:30
$begingroup$
No, I don't, but I hoped some one knows an algorithm, which could tell me if one exists and, if so, which prime it is.
$endgroup$
– 91378246
Jan 26 at 19:34
1
$begingroup$
@91378246: such algorithm would have solved the factorization problem and broken RSA. Given some large integer (integers of the form $p-1$ are not really special) there is no simple (polynomial) way to get a divisor, but you may employ sieve methods (like the quadratic sieve) to find divisors in some range, then a primality test (AKS is polynomial, for instance) to select prime divisors. Anyway, it will be computationally expensive.
$endgroup$
– Jack D'Aurizio
Jan 27 at 0:47
$begingroup$
Thank you very much, I will look into that.
$endgroup$
– 91378246
Jan 27 at 12:45
add a comment |
1
$begingroup$
Do you know that such a prime exists in your case? Usually it won't.
$endgroup$
– quid♦
Jan 26 at 19:30
$begingroup$
No, I don't, but I hoped some one knows an algorithm, which could tell me if one exists and, if so, which prime it is.
$endgroup$
– 91378246
Jan 26 at 19:34
1
$begingroup$
@91378246: such algorithm would have solved the factorization problem and broken RSA. Given some large integer (integers of the form $p-1$ are not really special) there is no simple (polynomial) way to get a divisor, but you may employ sieve methods (like the quadratic sieve) to find divisors in some range, then a primality test (AKS is polynomial, for instance) to select prime divisors. Anyway, it will be computationally expensive.
$endgroup$
– Jack D'Aurizio
Jan 27 at 0:47
$begingroup$
Thank you very much, I will look into that.
$endgroup$
– 91378246
Jan 27 at 12:45
1
1
$begingroup$
Do you know that such a prime exists in your case? Usually it won't.
$endgroup$
– quid♦
Jan 26 at 19:30
$begingroup$
Do you know that such a prime exists in your case? Usually it won't.
$endgroup$
– quid♦
Jan 26 at 19:30
$begingroup$
No, I don't, but I hoped some one knows an algorithm, which could tell me if one exists and, if so, which prime it is.
$endgroup$
– 91378246
Jan 26 at 19:34
$begingroup$
No, I don't, but I hoped some one knows an algorithm, which could tell me if one exists and, if so, which prime it is.
$endgroup$
– 91378246
Jan 26 at 19:34
1
1
$begingroup$
@91378246: such algorithm would have solved the factorization problem and broken RSA. Given some large integer (integers of the form $p-1$ are not really special) there is no simple (polynomial) way to get a divisor, but you may employ sieve methods (like the quadratic sieve) to find divisors in some range, then a primality test (AKS is polynomial, for instance) to select prime divisors. Anyway, it will be computationally expensive.
$endgroup$
– Jack D'Aurizio
Jan 27 at 0:47
$begingroup$
@91378246: such algorithm would have solved the factorization problem and broken RSA. Given some large integer (integers of the form $p-1$ are not really special) there is no simple (polynomial) way to get a divisor, but you may employ sieve methods (like the quadratic sieve) to find divisors in some range, then a primality test (AKS is polynomial, for instance) to select prime divisors. Anyway, it will be computationally expensive.
$endgroup$
– Jack D'Aurizio
Jan 27 at 0:47
$begingroup$
Thank you very much, I will look into that.
$endgroup$
– 91378246
Jan 27 at 12:45
$begingroup$
Thank you very much, I will look into that.
$endgroup$
– 91378246
Jan 27 at 12:45
add a comment |
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1
$begingroup$
Do you know that such a prime exists in your case? Usually it won't.
$endgroup$
– quid♦
Jan 26 at 19:30
$begingroup$
No, I don't, but I hoped some one knows an algorithm, which could tell me if one exists and, if so, which prime it is.
$endgroup$
– 91378246
Jan 26 at 19:34
1
$begingroup$
@91378246: such algorithm would have solved the factorization problem and broken RSA. Given some large integer (integers of the form $p-1$ are not really special) there is no simple (polynomial) way to get a divisor, but you may employ sieve methods (like the quadratic sieve) to find divisors in some range, then a primality test (AKS is polynomial, for instance) to select prime divisors. Anyway, it will be computationally expensive.
$endgroup$
– Jack D'Aurizio
Jan 27 at 0:47
$begingroup$
Thank you very much, I will look into that.
$endgroup$
– 91378246
Jan 27 at 12:45